Numerical methods for solving a class of fractional models

Fractional derivative operator is a useful theoretical discipline that is used by some of mathematicians for modeling and simulating many systems and processors based on the description of their properties. The main advantage of fractional derivatives in comparison with classical models with integer order is modeling many mechanical and electrical phenomena. One of these phenomena is fractional advection dispersion model (FADM). The present study investigates 5 classes of these models. Methods for solving these models are presented using Caputo fractional derivatives, Riemann-Lioville and Riesz. These methods are classified into two sections: numerical and analytic. The present study mainly focuses on numerical methods. The implicit numerical methods attracted more attention. Examples are solved using MATLAB. These methods are unconditionally stable and convergent.

کلیدواژه ها:

Fractional differential equation ، Implicit numerical methods ، Stability ، Convergence